Zero-energy states in the Kitaev finite and semi-infinite model

Авторы: Chuburin Yu P., Tinyukova T.S.
Журнал: Physica E
Том: 146
Год издания: 2023
Первая страница: 115528
DOI: 10.1016/j.physe.2022.115528
Аннотация: The Kitaev chain models a 𝑝-wave superconductor and hosts two Majorana bound states at the ends of the chain in the topological phase, for example if 𝜇 = 0, 𝛥 = 𝑡, where 𝜇, 𝛥 and 𝑡 are chemical potential, superconducting pairing potential, and the next-nearest neighbor hopping amplitude, respectively. We consider finite and semiinfinite chains with close parameters 𝜇 = 0 and 𝛥 = 𝑡 + 𝜀 where 𝜀 is small, near the point 𝛥 − 𝑡 = 0. Using the Dyson equation and the Green’s function for the infinite Kitaev chain, we analytically study the conditions for the appearance of zero-energy states, as well as their wave functions. We have proven that in the finite chain such states exist only if 𝛥 > 𝑡 and the number of sites is odd. Zero-energy states disappear in the finite chain in the presence of an impurity potential, which indicates their instability. But in the semi-infinite chain, for 𝛥 > 𝑡 there is a single Majorana state and it is robust against an impurity.Thus the bulk-boundary correspondence may be violated for the Kitaev chain near the singular point.
Добавил в систему: Чубурин Юрий Павлович

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